Eccentric chap primarily inducing anxious state (8)
I believe the answer is:
cambodia
'state' is the definition.
(Cambodia is an example)
'eccentric chap primarily inducing anxious' is the wordplay.
'eccentric' becomes 'cam' (an eccentric is a mechanical device such as a cam).
'chap' becomes 'bod' (I've seen this in other clues).
'primarily' suggests taking the first letters.
The first letters of 'inducing anxious' is 'ia'.
'cam'+'bod'+'ia'='CAMBODIA'
(Other definitions for cambodia that I've seen before include "SW Asian state" , "Southeast Asian country" , "Kampuchea before 1975" , "Country of SE Asia" , "Country of SW Asia, capital Phnom Penh" .)