Greek character worried over following Britain's lead (4)
I believe the answer is:
'greek character' is the definition.
(letter from the Greek alphabet)
'worried over following britain's lead' is the wordplay.
'worried' becomes 'ate' (something worrying may eat someone up**).
'over' says the letters should be written in reverse.
'following' is a charade indicator (letters next to each other).
'lead' indicates taking the first letters.
The initial letter of 'britains' is 'b'.
'ate' back-to-front is 'eta'.
'eta' after 'b' is 'BETA'.
(Other definitions for beta that I've seen before include "final test" , "Second Greek letter - beat that" , "less than perfect mark" , "Second highest grade of mark" , "It's next after alpha" .)