Probably you know that a Hanja character may have more than one pronunciation. For example, 樂 has seven different pronunciations, 락, 악, 낙, 요, 료, 록, 로. (낙 is derived by the word-initial rule 두음법칙 applied to 락. 료, 록, 로 are very rare readings which have few usage, mostly for reading particular phrases in classical Chinese texts.)
When a Hanja character can be read in more than one way, its pronunciation for a particular word is decided either by pronunciation rules (which are quite regular and predictable), or by difference in meanings. (For example, 樂 means 'joyful' when read 락, 'music' when read 악, and 'to like or enjoy' when read 요.) Given a word, it is rarely the case that a Hanja character can be read in more than one way. Either it will violate a pronunciation rule, or end up in an awkward meaning when pronounced in a way different from the "correct" one. However, there are very few words when this happens. That is, more than one meaning of a character can be used to make sense of the word, ending up in a different pronunciation of it.
One example is 更新. 更 is read either 경 or 갱. When read 경, it means 'to fix, replace, or change'. ('고칠 경') When read 갱, it means 'to repeat, or to do something again'. ('다시 경') The second character 新 basically means 'new', and has a unique reading 신.
So 갱신(更新) means 'to do something again to make it new', as in renewing a house rent at the end of the contract. You would say "계약을 갱신하다" in Korean, 계약 being contract.
On the other hand, 경신(更新) literally means 'to replace a thing with something new, and it usually means 'to break a record (and make a newer high score).' You would say "기록을 경신하다" in Korean, 기록 being record.
In some other cases, the choice of pronunciation becomes arbitrary. One example is about the character 暴. It has a wide range of meanings, and has three different pronunciations, 폭, 포, and 박. When it means 'violent or fierce', it can be pronounced either 폭 or 포 ('사나울 폭/포'). A handful of words with the character allows arbitrary choice between 폭 and 포, while others have a fixed reading. One of those words is 흉폭(凶暴). 凶 means 'brutal', and the word means 'brutal and violent.' It can be read as either 흉포 or 흉폭.
To summarize, it is VERY rare for a Sino-Korean word of same characters have more than one pronunciation, but there are a few cases. The different reading may be because of a different meaning, or may just be open to arbitrary choice.