Give approval to at last, or half seem to (7)
I believe the answer is:
endorse
'give approval to' is the definition.
(I've seen this before)
'at last or half seem to' is the wordplay.
'at' says to put letters next to each other.
'last' indicates one should take the final letters.
'half' means to take half the letters.
'to' becomes 'endo' (I can't justify this - if you can you should believe this answer much more).
The last letter of 'or' is 'r'.
'seem' with half the letters taken is 'se'.
'r'+'se'='rse'
'rse' after 'endo' is 'ENDORSE'.
Can you help me to learn more?
(Other definitions for endorse that I've seen before include "No reeds (anag)" , "Give one's approval to" , "Put one's name to, approve" , "Sanction -- red nose (anag)" , "'Approve of, back (7)'" .)