If every item has the same format (\d?\d)h(\d{2}) then we can do the following :
First we need a function to convert the string to an object or something we can work with, I'll go with an object :
function timeStringToObj(str){
  var re = "^(\d?\d)h(\d\d)$";
  var h = str.replace(re, "$1");
  var m = str.replace(re, "$2");
  return {
    hours: parseInt(h),
    minutes: parseInt(m)
  };
}
Then we will need to ensure that the array is sorted, for instance "9h15" < "9h16" therefore "9h15"'s index is < "9h16"'s index , (if not use array.sort(/*some sorting function if necessary*/)) and loop through it to find the spot (I'll use a function of course), I'll consider your array as a global variable :
/**
*@param timeObjA an object that is the return value of a call of timeStringToObj
*@param timeObjB an object that is the return value of a call of timeStringToObj
*/
function AgeB(timeObjA, timeObjB){//A greater than or equal to B
  return (timeObjA.hours >= timeObjB.hours && timeObjA.minutes >= timeObjB.minutes);
}
/**
*@param a an object that is the return value of a call of timeStringToObj
*@param b an object that is the return value of a call of timeStringToObj
*/
function AleB(a, b){//A less than or equal to B
  return (timeObjA.hours <= timeObjB.hours && timeObjA.minutes <= timeObjB.minutes);
}
function putInTimeArray(str){
  var val = timeStringToObj(str);
  for(let i = 0 ; i < array.length ; i+=1){
    var curr = timeStringToObj(array[i]);
    //first check : elem >= last
    if( AgeB(val, curr) && i===(array.length-1) ){
      array.push(str);
      return true;
    }
    //second check : elem <= first
    if( AleB(val, curr) && i===0 ){
     array.unshift(str);
     return true;
    }
    //last check : first < elem < last
    if(i!=0 && i!=(array.length - 1)){
      if(AgeB(val, curr)){
        array.splice(i+1,0,str);
        return true;
      }
      if(AleB(val, curr){
        array.splice(i-1,0,str);//here i-1 is safe since i!=0 (condition)
        return true;
      }
    }//end of last check
  }//end of for-loop
}//end of function
If you're having doubts regarding my usage of splice please refer to this : How to insert an item into an array at a specific index?
EDIT
You'll probably need a more sophisticated regex to be more appropriate be this will do the job just fine if you don't go that crazy with those strings