Father near missing the start of hymn of praise (5)
I believe the answer is:
paean
'hymn of praise' is the definition.
(song of praise)
'father near missing the start' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'near' becomes 'mean' (both can mean miserly).
'missing the start' means to remove the first letter.
'mean' with its initial letter taken away is 'ean'.
'pa'+'ean'='PAEAN'
'of' is the link.
(Other definitions for paean that I've seen before include "Panegyric" , "Anthem" , "Encomium, eulogy" , "A song of triumph or praise" , "Song of thanksgiving" .)