Felt hat might be seen in The Arcadia regularly (5)
I believe the answer is:
terai
'felt hat' is the definition.
'terai' can be an answer for 'hat' (I have seen 'A hat' mean 'terai' so perhaps 'hat' could also mean 'terai'). I'm not sure about the 'felt' bit.
'seen in the arcadia regularly' is the wordplay.
'seen in' becomes 'te' (I can't justify this - if you can you should give a lot more credence to this answer).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternating letters of 'arcadia' are 'rai'.
'te'+'rai'='TERAI'
'might be' is the link.
Can you help me to learn more?
(Other definitions for terai that I've seen before include "Wide-brimmed ventilated felt hat of India" , "sun hat" , "sunhat" , "subtropical headgear" .)