Hi David,
4d - your reference to Andy if correct. 4 letter "apartment" ' + 3 letter "better" as in to outdo.
15a - 5 letter "clear" as in 'evident' or 'not concealed' with the "absolutely minimal amount of money" being 1,1 with the definition being "leave too much" - I would have thought the answer is 2 words but no doubt the editor has checked it.
13d - is a straight anagram with the definition being "authority"