Half-hearted private investigator obstructs old rocker (5)
I believe the answer is:
tepid
'half-hearted' is the definition.
(I've seen this in another clue)
'private investigator obstructs old rocker' is the wordplay.
'private investigator' becomes 'PI' (abbreviation).
'obstructs' is an insertion indicator (inserted letters interrupt or obstruct the word).
'old rocker' becomes 'ted' (Teddy boys were a subculture associated with rock).
'pi' going inside 'ted' is 'TEPID'.
(Other definitions for tepid that I've seen before include "lacking enthusiasm" , "Luke warm" , "Not very warm (water)" , "Moderately warm" , "Slightly warm" .)