The topic is often dropped in conversational Korean because it is already given context.
This sentence assumes you are directly asking someone their age, which is common when first meeting someone new so people can apply the proper level of respect in speech. In this, listeners already know what the topic of the conversation is, so it isn't needed to be understood.
연세 is the honorific replacement for 살 so you would use that word (and this question form) when talking to/about anyone who deserves honor or who you want to highly esteem, e.g. grandparents, your boss, a stranger you want to highly esteem. Otherwise if you're talking to/about someone who's not much much older and not much much more important then it's still respectful to ask 몇 살이에요?