Hi, not sure about claiming expenses after leaving an insurer but I am certain you can change to any health insurer at any time without penalty or loss of benefit or incurring a waiting period. Hibernian health have an offer this month and I believe this offer will reduce the cost of cover on two dates at end of month - if you want I can check out those dates but ring your local hibernian insurance broker and if they do business with hibernian health they should be aware of the offer this month. Note: A health insurer cannot bind you into a health insurance policy for a contract term eg 12 months - suggest if they try that with you seek information from the financial regulator or insurance omb office in Dublin - google their contact details
hope this helps.