Batman, say, might drink here or off one's trolley (9)
I believe the answer is:
superhero
'off one's trolley' is the definition.
The definition suggests a singular noun which matches the answer.
'batman say might drink here' is the wordplay.
I cannot quite understand how this works, but
'drink' could be 'sup' (to sup is to drink) and 'sup' is located in the answer.
an anagram of 'here' is 'erhe' which is located in the answer.
This explanation may well be incorrect...
'or' is the link.
Can you help me to learn more?
(Other definitions for superhero that I've seen before include "I'm often seen in a cape" , "comic book creation" , "Fantastic character" , "person who catches lots of baddies" , "One possibly involved in saving" .)