You are then faced with two options. If you're reasonably competent you can strip your phone and replace the SIM tray. If you're not then you can take the phone to a repair shop and pay an inflated price for someone to replace it for you. On some phones the SIM tray is soldered to the main board and the cost of replacement is greater than that of replacing the phone.
There is another option, if you can see your SIM tray and it's not buried in the device with a dedicated carrier tray. It's very easy and, with a little care it's a repair that can be effected by just about anybody. The only tools you will need are a pair of sharp nail scissors and a needle.
Your SIM card and phone are connected by two sets of three contacts. In the image you can see three of them, exposed at the bottom of the tray. The other three are hidden behind the shield, with their general location indicated by the orange arrow.
These second set of contacts are only affixed to the phone at one end and repeated removal and replacement of a nano-SIM card in a micro-SIM adapter will gradually push them down until they no longer make contact, or if they catch on the adapter, get folded over so they no longer connect to the right part of the SIM.
Make sure you're phone is unplugged and battery either removed or discharged before starting.
Remove your SIM (very carefully if it's sticking) then take your nail scissors and cut the shielding as shown by the two red lines in the picture. Very gently fold the shield up until you can see the three hidden contacts. You must make sure that you don't apply too much force as you'll need to fold the shield back down so that it holds the SIM against the contacts once you've done.
Once you can see the three hidden contacts take your needle and gently lift the contacts up (if they've been pushed down) or unfold them (if they've been folded over). Fold the shield back into place and re-insert the SIM card. You may need to employ a bit of trial and error to get the contacts in exactly the right place but if you look at the bottom of your SIM you can identify the six contact points and use them as a guide for where the contacts should be.
Whilst this trick won't work 100% of the time it can prevent a large repair bill if done carefully. As ever I take no responsibility for any failures or problems - only undertake this repair only if you know what you're doing and are confident with the tools at hand.