ClearAll["Global`*"];
f[x_, y_] := x + y^-1;
p = ContourPlot[
f[x, y], {x, -5, 5}, {y, -5, 5},
Contours -> 10,
ContourLabels -> True,
LabelStyle -> {Directive[Bold, Medium], White,
RotateLabel -> True},
ImageSize -> Large
]

f[x_, y_] := x + y^-1
t[x_, y_] = Grad[f[x, y], {x, y}] . {{0, -1}, {1, 0}};

ContourPlot[
    f[x, y],
    {x,-5,5},
    {y,-5,5},
    Contours->10,
    ContourLabels->Function[{x,y,z},Text[z,{x,y},{0,0},t[x,y], BaseStyle->FontColor->White]]
]