There are many private health funds. Levels of cover, types of cover and costs of cover vary, so it is up to each individual to clarify with their Fund whether they are covered for Psychological services, and to what extent.
Some Funds provide a different of cover for Clinical Psychology, than for other Psychology endorsements. My endorsements are with Counselling, and Educational & Developmental. While some Funds do not differentiate, others do and one may wish to consult one’s Fund.
It is more rare, but possible under some cover programs in some Funds, to be covered specifically for Psychotherapy. You may wish to check with your Fund.