Pete Davidson Kate Beckinsale Holding Hands After His Comedy Set in L.A.

Pete Davidson and Kate Beckinsale sure seemed like a couple Friday night as they left his stand up shows in West Hollywood.

The 25-year-old 'SNL' star held on tight to 45-year-old Kate as they left the Coronet theater. They then beelined it to their hotel in Santa Monica.

Pete -- who did 2 shows as Kate looked on -- has been doing great.

Davidson's clearly back in circulation ... he's fully back on 'SNL' following his troubling Instagram back in December. He's been out and about with best bud, Machine Gun Kelly.

As for history ... Ariana Grande and Pete called off their engagement October 14. As for Kate, her husband, Len Wiseman, filed for divorce in 2016. It's unclear if the divorce has become final.