You ask a simple question, but the answer is detailed, depending on how you are adding the extra tracks and what they are created from (midi, samples, live instruments, vocals).
You do not need to record from iReal Pro to a recording app necessarily (see below for some information on this) because you can export the audio file of a song. Set metronome if it is necessary (for your count in for recording the other tracks) and other player settings (like key, tempo, mixer volumes or mute etc.) Then Send >Audio … as wav.

Tap, Share, then Open in…
Choose a recording app to add the track to. You have many options for apps, here are four:
Garageband is free to download on recent iOS devices. Has virtual instruments, guitar pedal effects, midi etc. for your additional tracks.
Cubasis offers more professional DAW features and design (might be more suitable for you if you are used to using a DAW on your computer). It has a large number of sounds and synths. Like GB, midi support.
Auria is more a recording app (midi to come). It would be more useful for you if you only want to record tracks live. The quality of the effects are very high. If you are used to ProTools, then this is similar. You can add many tracks (some apps are limited to 8) if needed.
If you are a guitarist, another app you might be interested in is Amplitube which has a recording section (in-app purchase) and some great amp simulations but of course you can add other instruments or vocals on other tracks also.
The audio file is usually imported into the recording app ready for import to a specified track (not imported directly) as you have to select a track, a start point in the timeline and which audio file to add.

For the additional tracks, what are they recorded from?
The built-in mic on the iPad is not high quality but useful for demos. Using an audio interface is best for direct recording guitars or from a quality microphone (using the interface’s mic preamp).
Not all interfaces will work with iPad, so check on a site such as Auria’s. If it works with one app, other similar recording apps should be able to use it also.
Simple interfaces like iRig Pro may be all you need if you only need one input, but the multi-input interfaces provide more flexibility, stereo, recording on more than one track simultaneously etc.
If you want to use an app with a virtual keyboard or fretboard etc, GB or Cubasis would be good for other tracks you are adding.

Check out Audiobus. You can route iReal Pro’s audio output live (as it is playing) to a recording app (an effects app can be used in-between if useful but it is applied to the complete audio). Not all apps are able to be used with Audiobus, but all the major ones (and many many others) do. This is probably what you had in mind, pressing play in iReal Pro, then it recording into a recording app. Apps like Auria can do this. (I tend to use audio file export, not really needing to use Audiobus for this part).
Then you can record your additional tracks using Audiobus if you need to, perhaps a mic into an effects app then into a track in your recording app. Or just record the additional tracks directly from the recording app.


Links:
http://www.steinberg.net/en/products...s/cubasis.html
http://www.auriaapp.com/Products/auria
http://auriaapp.com/Support/auria-audio-interfaces
http://www.ikmultimedia.com/products/amplitubeipad/
http://www.ikmultimedia.com/products/atstudio/
http://audiob.us

Once mixed down, you can either send to your computer, perhaps add MP3 tags, add to iTunes then copy to your iPad music folder (maybe into a playlists); or use ForScore app (or similar) where you can view a PDF (lyrics, an iReal Pro chart, or notation for melody) and attach the audio file which can be played from viewing that page(s) depending on how you have set them up. (ForScore can either link to your music (audio files) folder or import the audio files into itself for you to attach to the PDF pages. It is a musician’s app, so allows you set lists, search, categories, composer, genre, key etc. to help organise.)
http://forscore.co

You should be able to find other audio players you can use also, perhaps not necessarily designed for musicians playing live but just as suited for what you are doing.

Obviously this is just giving you an idea of the possibilities. If you have further questions, post back here. You have not given us much information to reply specifically to your situation. Hopefully others here at the forum will let you know what they do for their purposes.

Also run searches in this forum (top right) for keywords as they are other threads on some of the apps mentioned here.