Firm head welcoming youth leader’s modesty (7)
I believe the answer is:
coyness
'modesty' is the definition.
(I've seen this in another clue)
'firm head welcoming youth leader's' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'head' becomes 'ness' (ness is a headland).
'welcoming' means one lot of letters goes inside another (in sense of 'inviting in').
'youth leader' becomes 'y' (I've seen this in other clues).
'co'+'ness'='coness'
'coness' enclosing 'y' is 'COYNESS'.
(Other definitions for coyness that I've seen before include "Demureness" , "Affected modesty" , "Arch reticence" , "Pretended modesty" , "Shyness" .)