Google Apps Script for Multiple Find and Replace in Google Sheets

Each time you call getValues and setValues in your script there is a considerable overhead cost involved and slows your script down. (Google app script timeout ~ 5 minutes?) I modified your above script to make that 1 call for getValues and 1 Call to setValues. The code applies all the replacement to the array in memory before pasting your modified timetable back to the sheet.

function runReplaceInSheet(){
  var sheet = SpreadsheetApp.getActiveSpreadsheet().getSheetByName("StudentTimetableEntry");
  //  get the current data range values as an array
  //  Fewer calls to access the sheet -> lower overhead 
  var values = sheet.getDataRange().getValues();  

  // Replace Subject Names
  replaceInSheet(values, /\d\dART\d\d/g, "Art");
  replaceInSheet(values, /\d\dCCL\d\d/g, "Communication & Culture");
  replaceInSheet(values, /\d\dDLT\d\d/g, "Digital Technology");
  replaceInSheet(values, /\d\dDRA\d\d/g, "Drama");

  // Replace Staff Names
  replaceInSheet(values, 'TED', 'Tahlee Edward');
  replaceInSheet(values, 'TLL', 'Tyrone LLoyd');
  replaceInSheet(values, 'TMA', 'Timothy Mahone');
  replaceInSheet(values, 'TQU', 'Tom Quebec');

  // Write all updated values to the sheet, at once
  sheet.getDataRange().setValues(values);
}

function replaceInSheet(values, to_replace, replace_with) {
  //loop over the rows in the array
  for(var row in values){
    //use Array.map to execute a replace call on each of the cells in the row.
    var replaced_values = values[row].map(function(original_value) {
      return original_value.toString().replace(to_replace,replace_with);
    });

    //replace the original row values with the replaced values
    values[row] = replaced_values;
  }
}

Give this code a try, if you still have issues with timeouts, my suggestion is setup triggers to help chain functions.