Seeming only half keen to many, perhaps, he nevertheless is important (3,3)

'seeming only half keen to many' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'he nevertheless is important' is the wordplay.
I cannot quite see how this works, but
'he' could be 'man' (I've seen this in another clue) and 'man' is found within the answer.
'important' could be 'key' (similar in meaning) and 'key' is found in the answer.
This accounts for all the letters.
This explanation may well be incorrect...

'perhaps' is the link.

Can you help me to learn more?