Answer
The gravitational field strength will increase on the surface of a shrinking star. The star is getting smaller while its mass M remains the same, i.e., the star's mass is becoming compacted.
Work Step by Step
Consider the force on a body at the surface of the star.
Newton's law of gravitation tells us that the gravitational attraction is $F = G \frac{Mm}{d^{2}}$.
As the star collapses, d decreases while M and m stay constant, so the force increases.