Intrude by stealth, or chance, after straying (8)
I believe the answer is:
encroach
'intrude by stealth' is the definition.
'encroach' can be an answer for 'intrude' (I've seen this before). I'm not certain of the 'by stealth' bit.
'or chance after straying' is the wordplay.
'after straying' is an anagram indicator.
'or'+'chance'='orchance'
'orchance' is an anagram of 'ENCROACH'.
Can you help me to learn more?
(Other definitions for encroach that I've seen before include "Go past a normal limit" , "Gradually intrude (upon another's space)" , "Enter upon another's property or rights" , "Tread on someone's toes" , "Gradually intrude (on person's area)" .)