The classical approach is to repair the ends using a DNA polymerase so that you have blunt ends that can be ligated Alternatively, add synthetic oligonucleotides to modify the ends to make them compatible with your target vector/other DNA molecule.
NEB market a very efficient rapid end repair kit. You can put together your own from basic components. Most often Klenow enzyme or T4 DNA polymerase is used. However, if you have to purchase all the components it can work our cheaper to buy the kit.
Just to follow up on my previous answer. Don't use too much Klenow enzyme in your fill in as it can affect the efficiency of the subsequent ligation. I tested this years' ago by rqadiolabelling the ends of a fill in reaction on DNA and found that too much enzyme reduced label incorporation. It also affected subsequent ligation.
End removal or fill-in can be accomplished using a number of enzymes, including DNA Polymerase I Large (Klenow) Fragment, T4 DNA Polymerase or Mung Bean Nuclease. these approaches are very easy to perform, you just need a buffer and a enzyme.
you can also try other approach just like gibson assembly.
If you know the exact gap sequence, a synthetic oligonucleotide can be tailored to fill the gap, after annealing, ligation is possible. If a nick remains, it can be repaired before transformation or repaired by the transformed cell itself.