Clue: Mix a Puerto Rican cocktail for nearby star (7,8)
Answer: PROXIMA CENTAURI
Explanation: Definition: nearby star
An anagram ('cocktail') of 'mix a Puerto Rican', for the nearest known star to our fair Earth; a mere 4.2465 light-years distant (that's around 4.0172 x 10¹³ km. Or 2.497 x 10¹³ miles, give or take).