Hi zoes, and welcome to the forum
There are several car insurance companies in Malta- you can find them by googling - atleast one gives quotes online, but you are better off calling them due to your circumstances (2nd driver under 21 and not resident in Malta). Not all the insurance companies accept NCB from overseas - there are a couple of companies that do that are listed on the "recommended suppliers" forum, which costs £25 a year to join, with 50% going to Gozo SPCA. There is no compuslion to subscribe, but thats the only place companies are allowed to be recommended
How old is your partner ?
ps I presume the registration tax on a 1 year old BMW 320d is going to be very high (more than € 10,000 ??)