Greek character worried over following Britain's lead (4)
I believe the answer is:
Here is my best explanation:
'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 "Old character", "Alpha, --, gamma", "Second highest grade of mark", "less than perfect mark", "Second Greek letter, B", "It's next after alpha", "second class grade?", "Character between alpha and gamma", "Second-class" and "Greek 'b'".)