Greek character worried over following Britain's lead (4)
I believe the answer is:
Here is my best explanation:
'greek character' is the definition.
'worried over following britain's lead' is the subsidiary indication.
'worried' becomes 'ate' (eating is a kind of worrying).
'over' shows that the letters should be reversed in order.
'following' says to put letters next to each other.
'lead' suggests taking the first letters.
The initial letter of 'britains' is 'b'.
'ate' in reverse letter order is 'eta'.
'eta' put after 'b' is 'beta'.
(Other definitions for beta that I've seen before include "The Greek letter B", "Letter before gamma", "Character between alpha and gamma", "Greek 'b'", "Second Greek letter - beat that", "The second Greek letter", "Second highest grade of mark", "Second Greek letter, B", "Greek character - not quite top-notch" and "In a constellation, a star second in brightness".)