If I were a heel, then as soon as it started to look like I was about to lose a match, I'd slap the referee or nut-punch my opponent or get myself counted out to retain my championship (assuming I had one.)
If I were a debuting wrestler, then I'd also do Crayo's idea, and go after a main eventer player and cost him a big match like a championship bout or some other match of equal importance. It's using DDP's logic when he stalked Undertaker's (ex) wife Sara upon arriving in WWF in 2001 - if you want to make a big impact, then you go after the biggest dog in the yard.