Trojan regularly declining acting sycophantically (8)

I believe the answer is:

toadying

'acting sycophantically' is the definition.
(to toady is to act sycophantically)

'trojan regularly declining' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'declining' becomes 'dying' (similar in meaning).
The alternate letters of 'trojan' are 'toa'.
'toa'+'dying'='TOADYING'

(Another definition for toadying that I've seen is " Obsequious".)

I've seen this clue in The Telegraph.

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