Update Trigger conditional values - sql-server

Question

I have been searching around stackoverflow but I have not found what I'm looking for.
I have a Sql Server Database. One table with a field "Priority" I would like to update on every insert or update.
The problem is that I want to perform a Priority pile using this rules:
1.-If the value I try to insert has a prority value that already exists then every consecutive row in the table must change its priority value adding 1.
2.-If the value I try to insert has a priority that not exists then the trigger does nothing.
This is the trigger I haver built:
ALTER trigger [Priority]
on [dbo].[TBL_PILA]
after insert, update
AS
declare #priority int;
declare #reg_id int;
SELECT #reg_id =i.id from inserted i;
SELECT #priority =PRIORITY from TBL_PILA where ID =#reg_id
-- perform update here in TBL_PILA table
UPDATE TBL_PILA SET PRIORITY=PRIORITY+1 WHERE ID <>#reg_id AND PRIORITY>=#priority
GO
Edit: As Suggestions, I change the trigger body like this:
ALTER trigger [Priority]
on [dbo].[TBL_PILA]
after insert, update
if exists (select *
from inserted i join TBL_PILA m
on i.ID = m.ID
)
update TBL_PILA set PRIORITY = PRIORITY + 1
where exists (select * from inserted i
join TBL_PILA m
on i.ID = m.ID
where m.PRIORITY>=i.PRIORITY)
Now I have a new problem: the priority value inserted is affected by the trigger and it is added 1 too.
Does anybody knows how to increase priority values only affecting some range as I explained below?
The problem is whenever exists a few consecutive values and one not consecutive value the trigger must stops.
Example
Priority 1 2 4 5 6 8
If I try to insert a row with priority=3 the result should be:
1 2 3 4 5 6 8
Then If I try to insert a row with priority=4 then the result should be:
1 2 3 4 (inserted value) 5 (4+1) 6 (5+1) 7 (6+1) 8
But using the trigger I built I get this: 1 2 3 4 5 6 7 9 (8+1)