The old swine at first gives thumbs-up (3)
I believe the answer is:
yes
'thumbs-up' is the definition.
(I've seen this in another clue)
'the old swine at first' is the wordplay.
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'at first' suggests taking the first letters.
The first letter of 'swine' is 's'.
'ye'+'s'='YES'
'gives' is the link.
(Other definitions for yes that I've seen before include "Positive response" , "Oui" , "Aye" , "I agree" , "Affirmative answer" .)