Assuming your function has the name f, you can use clear f; to clear persistent variables within f.
Like here:
function f()
persistent p
if isempty(p)
p = 42;
fprintf('p was empty, now p == %g\n',p)
else
p = p+1;
fprintf('p == %g\n',p);
end
end
If you then execute
f();
f();
f();
clear f;
f();
f();
you will get
p was empty, now p == 42
p == 43
p == 44
p was empty, now p == 42
p == 43
