Curiously nosy, turned up my name or an equivalent term (7)
I believe the answer is:
synonym
'an equivalent term' is the definition.
'curiously nosy turned up my name' is the wordplay.
'curiously' indicates anagramming the letters.
'turned up' shows that the letters should be reversed in order.
'name' becomes 'n' (common abbreviation e.g. on forms).
'my'+'n'='myn'
'myn' reversed gives 'nym'.
'nosy' is an anagram of 'syno'.
'syno'+'nym'='SYNONYM'
'or' is the link.
(Other definitions for synonym that I've seen before include "My sonny (anag)" , "Word with meaning similar to that of another" , "text with similar import" , "Word that can be exchanged for another" , "Substitute brought in for a term" .)