Edit: Uhmmm...what the other guys said. Too slow on the draw composing my reply!
Compression is your friend. It should allow you to get the applause no louder than the loudest music section which should make for tolerable listening.
[1] Find the loudest music peak
[2] Amplify | Dynamics Processing
[3] Set your threshold to the loudest music peak
[4] Set your compression ratio (in this case, compress the snot out of everything with a high ration, > 20:1 - I find this accomplishes much the same effect but sounds better than hard limiting, which is another function in CEP that IMO sounds like shit)
[5] Amplify as normal to get levels up.
So, for example, if the music peaks at -20dB, you'd go into Dynamics Processing and select Compress from the dropdown, set your ratio to 10:1, and set the threshold at -20dB. In the next row, select the Flat dropdown. Done. It'll read something like Compress 20:1 above -20dB, Flat below -20dB. Then amplify the whole thing.
Play with different ratios / attack / decay to find what sounds best to your ears.