If the balance transfer limit isn’t high enough, you have two options:
Move what you can onto the new card, and pay off that and any remaining balance on your old card.
Apply for another card from a different provider in the hope that you’re offered a higher limit. However, you run the risk that multiple credit checks by card providers over a short period of time signal to other lenders that you’re having difficulties managing your finances. This can have a negative effect on your credit score. Spread your applications out over time.