Beginning to seem worried and anxious (6)
I believe the answer is:
scared
'anxious' is the definition.
(I've seen this before)
'beginning to seem worried' is the wordplay.
'beginning to' indicates taking the first letters.
'worried' becomes 'cared'.
The initial letter of 'seem' is 's'.
's'+'cared'='SCARED'
'and' acts as a link.
(Other definitions for scared that I've seen before include "having kittens" , "Frightened, alarmed" , "Afraid, anxious" , "Thing which precipitates an event" , "Frightened or apprehensive" .)