Figure out algorithm to numeric key generator with one known input and output
Ideally there would be some utility or a formula that I could apply or tweak here. 


I have to say there is no such utility, no such formula. This problem has no solution.

There is 10000! = factorial(10000) different transformations of 4-digit numbers to 4-digit numbers. For instance, your input 7153 and result 9533 can be produced by any of the following functions:

f(x)=(2x+5227) MOD 10000

f(x)=(3x+8074) MOD 10000

f(x)=(x^3+8956) MOD 10000


Knowing a single pair is not sufficient to find out what transformation was used. If they use some simple function, then having more pairs might give (without guarantee) an insight about this function.