Rare problem, having terribly dim fan (7)
I believe the answer is:
admirer
'fan' is the definition.
(an admirer is a fan of something)
'rare problem having terribly dim' is the wordplay.
'problem' indicates anagramming the letters.
'having' is an insertion indicator.
'terribly' indicates an anagram.
'rare' is an anagram of 'arer'.
'dim' anagrammed gives 'dmi'.
'arer' placed around 'dmi' is 'ADMIRER'.
(Other definitions for admirer that I've seen before include "One who cherishes, like boy friend" , "Married to suitor" , "Married to one who cherishes" , "potential suitor" , "Married to one who thinks highly of" .)