The star beginning to oscillate could become dimmer, possibly (8)
I believe the answer is:
rheostat
'dimmer possibly' is the definition.
(dimmer is a kind of rheostat)
'the star beginning to oscillate could become' is the wordplay.
'beginning to' suggests taking the first letters.
'could become' is an anagram indicator.
The first letter of 'oscillate' is 'o'.
'the'+'star'+'o'='thestaro'
'thestaro' anagrammed gives 'RHEOSTAT'.
(Other definitions for rheostat that I've seen before include "Current-changing device" , "Resistor for regulating current" , "The roast (anag.); electrical instrument" , "Variable resistor" , "showing some resistance" .)