A fellow member of my gym tried to find someone to take over her membership. She posted on Facebook in German, but also included the following English translation:
Hallo! Ich gebe meine Fitnessstudio-Mitgliedschaft ab. Bei Interesse gerne melden.
Hi! I’m giving away my gym membership. If you’re interested, let me know.
The problem is that “to give away” specifically implies that you don’t want anything in return. According to the Oxford English Dictionary:
to give something away: to give something as a gift
I’m sure it would be much easier to find someone to take your membership for free!