(defn min-pair-sum [nums]
  (let [sorted-nums (sort nums)
        n (count sorted-nums)]
    (loop [i 0
           j (dec n)
           max-pair-sum 0]
      (if (< i j)
        (recur (inc i) (dec j) (max max-pair-sum (+ (nth sorted-nums i) (nth sorted-nums j))))
        max-pair-sum))))

(println (min-pair-sum [3 5 2 3])) ; Should print 7

The min-pair-sum function takes a vector of integers nums as input. It first sorts the elements of the nums vector using the sort function. Then, it initializes variables i and j to represent the start and end indices of the sorted vector, respectively. The variable max-pair-sum is initialized to 0.

The function uses a loop (implemented with recur) to iterate over the sorted vector from both ends towards the center. Inside the loop, it calculates the sum of the elements at indices i and j and updates the max-pair-sum if the current sum is greater than the previous maximum. The loop continues until i becomes greater than or equal to j.

Finally, the function returns the minimum pair sum max-pair-sum.

The time complexity of this solution is O(n log n), where n is the number of elements in the input vector nums. This is because the sort operation has a time complexity of O(n log n) and the subsequent loop iterates over the sorted vector, which takes O(n) time. Therefore, the dominant factor is the sorting operation, resulting in an overall time complexity of O(n log n).

The space complexity of this solution is O(n) because we create a sorted copy of the input vector using sort, which requires additional space.