To slip through the net means to go unnoticed or undealt with, but in this context the speaker is saying that they will make sure another spook is noticed.
Consider the statement "Dee, as we are now on first name terms, I'm not letting another spook  be noticed and dealt with.". Based on this "Dee, as we are now obviously on first name terms, I'm not letting another spook slip through the net." a true statement? Yes, no, or I don't know?