The problem is that for some reason FourDivergence acting on DiracSlash gives 0.
In[2]:= fun=GS[p]//FCI
Out[2]= gs[p]
In[3]:= pa=FourVector[p,a];
In[4]:= FourDivergence[fun,pa]
Out[4]= 0
Here is a workaround:
In[5]:= fun2=DiracMatrix[b] FourVector[p,b]
Out[5]= ga[b] FourVector[p, b]
In[6]:= Contract[fun2]
Out[6]= gs[p]
In[7]:= FourDivergence[fun2,pa]
Out[7]= ga[a]
You can always use Contract afterward, if necessary.
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