pr := 2
f[x_,y_] := Sin[y]*Cos[x]
gradient[x_,y_] := {-Sin[y]Sin[x], Cos[y]Cos[x]}

dp :=DensityPlot[f[x,y],{x,-pr,pr},{y,-pr,pr},PlotRange->pr,ColorFunction->"TemperatureMap"]
gradientPlot:= VectorPlot[gradient[x,y],{x,-pr,pr},{y,-pr,pr},VectorScale->{.035,.9,None},VectorPoints->30,PlotRange->Automatic]
s:=Show[{dp,gradientPlot}]

s

gradientPlot:= VectorPlot[{-y,x},{x,-pr,pr},{y,-pr,pr},VectorScale->{.035,.9,None},VectorPoints->30,PlotRange->Automatic]

gradientPlot