Obsession, not initially serious, developed (8)
I believe the answer is:
neurosis
'obsession' is the definition.
(I've seen this before)
'not initially serious developed' is the wordplay.
'initially' suggests taking the first letters.
'developed' indicates anagramming the letters.
The initial letter of 'not' is 'n'.
'serious' is an anagram of 'eurosis'.
'n'+'eurosis'='NEUROSIS'
(Other definitions for neurosis that I've seen before include "Mental disorder of resinous origin" , "Mild condition such as obsessive behaviour" , "Resinous (anag) -- unspecific personality disturbance" , "So insure against the nervous disorder" , "Trouble in mind" .)