Makes time to welcome earl demanding serious attention (7)
I believe the answer is:
earnest
'serious attention' is the definition.
(I've seen this before)
'makes time to welcome earl' is the wordplay.
'makes' becomes 'earns' (as in making money).
'time' becomes 't' (abbreviation).
'to welcome' is an insertion indicator (inserted letters are welcomed in).
'earl' becomes 'e'.
'earns'+'t'='earnst'
'earnst' going around 'e' is 'EARNEST'.
'demanding' acts as a link.
(Other definitions for earnest that I've seen before include "Firm" , "Solemn; pledge" , "Serious; pledge" , "'Heartfelt, sincere (7)'" , "Sincere; enthusiastic" .)