June going topless as Dilys stripped anxiously (8)
I believe the answer is:
uneasily
'anxiously' is the definition.
(I know that anxiously can be written as uneasily)
'june going topless as dilys stripped' is the wordplay.
'going topless' means to remove the first letter.
'stripped' indicates the central letters (outside letters removed).
The middle letters of 'dilys' are 'ily'.
'june' with its first letter taken off is 'une'.
'une'+'as'+'ily'='UNEASILY'
(Other definitions for uneasily that I've seen before include "With anxiety or apprehension" , "In apprehensive manner" , "Hardly so, you might think" , "In nervous way" , "In worried way, lacking in confidence" .)