Yemen's population is estimated to age even further by 2050, with
57.3% of the population over the age of 60.
This is correct and stylistically appropriate. The first clause states a bald fact, with the second providing additional or clarifying information.
A less stylish approach might be to break the sentence and use "In fact" or "Actually" or "Indeed" in place of the "with". In fact, you can do this both with my paragraph and the original quote. Note that when using "with" in these examples there is clear anaphora (backward referencing) - the example picks up on 'the' population (definite article because already mentioned) while my paragraph picks up on 'first' clause and elides the word "clause" when referring to the 'second' [clause]. The word "with" introduces the anaphorical noun phrase.