The state hasn't had a low-cost provider of abortion services for more than a year, after the previous provider withdrew from Tasmania due to a lack of demand.

In the meantime, private specialists have been providing the service from Hobart.

On Friday, the rogue Speaker Ms Hickey held a hotly anticipated media conference where she announced she would be remaining in the Liberal Party after feeling she'd been spurned by her colleagues in not having been elevated to the ministry in the recent Cabinet reshuffle.

She will continue to provide the government with confidence and supply.

On Wednesday, Ms Hickey wrote to the new Health Minister asking to meet to discuss access to terminations in Tasmania, which the Speaker said she saw as "a legal right".

"Interim access has been available but a dedicated state-wide service is yet to be implemented," she said.

"I do hope that Minister Courtney can do better [in this area] than her predecessor [Michael Ferguson]."

Ms Courtney, who is also the new Minister for Women, said on Friday that Tasmanian women did have access to termination services right now but she was "looking forward" to talking to stakeholders about the issue.

"I'm very [mindful] to make sure that the provision of services to women and the support that they are provided in vulnerable times, [that] they do have full access to a suite of services," she said.

Independent Nelson MLC Meg Webb has also called on Ms Courtney to make access to terminations an immediate priority.