To access HMS Temeraire she should be able to access the gym with her Gym Membership Card. However be advised that this card is due for renewal annually, so check the date of expiry. Application forms are available from Temeraire (in person) or downloadable from their website on the intranet (DII only).
If your wife is intending to access the base (i.e. the Dockyard/HMS Nelson, not the Temerair site) she cannot use her HMS Temeraire pass, and should be in possession of a dependent's ID card. If you have not applied for one, contact the Pass Office at HMS Nelson Main Gate (next to the OOW Office) for further details.
Thanks for the reply. I did mean to access Temaraire as well. I have an application and its renewed every march, with half price fee for joining in October (£15). Thanks for the info on the dependants ID, I was wondering about that too, do u know if that's valid everywhere such as sultan, where I'm based, or just the dockyard?