Is it safe to connect battery in series with wall adapter?
You do NOT want to connect the battery in parallel with the wall adapter. The battery will most likely explode. 

It sounds like what you are asking is if you could wire them in SERIES. I.E. 10V + 3V = 13V. You could do this for some simple experimentation as long as the current of your load is much less than the rating of the battery or the wall adapter. However in the long run this is to be discouraged and you should obtain the wall adapter that gives you the voltage that you need.

You could also consider buying or building a switch mode up converter that takes your 10V up to 13V.