A colloquial expression meaning you have room for dessert even though you are full; figuratively, it can mean 'there's still room' or 'I can make an exception.'
夕食はお腹いっぱいだったが、ケーキなら別腹だ。
I was full after dinner, but I can still make room for cake.
ラーメンを食べた後に、彼は別腹だと言ってアイスを頼んだ。
After eating ramen, he said he had room and ordered ice cream.
食事のあとはいつも別腹で甘いものを食べる習慣がある。
He always has a habit of eating something sweet after a meal, claiming a separate stomach for desserts.
その話題には別腹で興味があるらしい。
He seems to have a special interest in that topic (figuratively, 'a separate appetite' for it).