Hi Sree

the way i see it, you have several issues with your code and logic.

regarding the code -

        1.you are not ready for Bulk insert (what if two tasks are inserted at the same time - via data loader or something)

2.you are not checking if the task is even related to an account record - since you are creating tasks in your AFTER               INSERT trigger - you potentially create an infinite loop.

regarding the logic - 

1.what if two tasks are inserted for the same account, which one is "Copied" to the newly created task?

in any case, here is the code for your logic, ready for bulk and checking that the task is related to account (just complete the multiple tasks part)

trigger AddTaskActivityToAccountTLA on Task (after insert) 
{
	Map<String,Schema.SobjectType> globalDescribe = Schema.getGlobalDescribe();
	String accPref = globalDescribe.get('Account').getDescribe().getkeyprefix();
	map<Id,List<Task>> accIds = new map<Id,List<Task>>();
	List<Task> newTasks = new List<Task>();
	
	/*
		iterate over trigger records -
		if a task is related to an account, put its account Id in a set for later
	*/
	for(Task t : trigger.new)
		if(t.WhatId != null && String.valueOf(t.WhatId).subString(0,3).equalsIgnoreCase(accPref))
			if(!accIds.containsKey(t.WhatId))
			{
				accIds.put(t.WhatId,new List<Task>{t});
			}
				
	//if any of the tasks inserted are related to an account - perform your logic
	if(!accIds.isEmpty())
	{
		List<AccountTLA__c> lst_accTLAs;
		try{
			lst_accTLAs = [select Id,Account__c from AccountTLA__c where Account__c IN: accIds.keySet()];
		}
		catch(QueryException e)
		{
			//found no account TLAs for the relevant accounts
		}
		
		if(lst_accTLAs != null && !lst_accTLAs.isEmpty())
		{
			for(AccountTLA__c accTLA : lst_accTLAs)
			{
				List<Task> account_newTasks = accIds.get(accTLA.Account__c);
				if(account_newTasks != null && !account_newTasks.isEmpty())
				{
					if(account_newTasks.size() > 1)
					{
						//what values do you want to give the new task you are creating, 
						//if more than one task was inserted in the bulk for this account???
					}
					else
					{
						//I'm assigning the fields that you mentioned in your post, but if the business scenario allows it
						// cloning the original task and just changing the whatId before insert would be easier!!!
						Task t = new Task(
											Type = account_newTasks[0].Type,
											OwnerId = account_newTasks[0].OwnerId,
											Subject = account_newTasks[0].Subject,
											ActivityDate = account_newTasks[0].ActivityDate,
											Status = account_newTasks[0].Status,
											Priority = account_newTasks[0].Priority,
											WhatId = accTLA.Id;
										 );
						newTasks.add(t);
					}
				}
				
			}
		}
		if(!newTasks.isEmpty())
			insert newTasks;
	}
}

Hope this helps.

if so, mark the issue as resolved.

Thanks