Several issues here that all need addressing, that have already been mentioned:
1. If the phone that you're putting the new sim card into, isn't on the the same network as the new sim card that you're using, then the phone will need unlocking.
2. If the sim cards are a different size, then you'll need to buy a converter. I think there are 3 different sizes of sim cards: normal, micro and nano. Do a search on Ebay for "sim converter". They're only a couple of quid ..... ish and they enable you to use a smaller size sim, in a phone that usually takes a larger size, by inserting the sim card into the converter, making it bigger than normal.
If you want to put a larger size sim, in a phone that usually takes smaller size sim cards .... I don't think it's possible.
3. If you're using a smart phone (such as the iPhone, etc), you'll need to make sure that the price plan of the new sim, includes a data useage. If you can't access the internet, a lot of the features on a smart phone, simply won't work properly.