Insert Triggers And Max Values

I have a situation where I need to create an insert trigger on table a which will create a corresponding record in table b. However before I insert the record i must obtain the max value for the record in table b and increment it by one. I have all this working. My question is if I just put a begin and commit with this statement is there a chance that when 2 users insert at the same time the max value may be incorrect say for instance

CREATE TRIGGER tr_cms_prov_ins ON provider
FOR INSERT
as
declare @ndentPrid char(3),
@nxtgenPrid char(7),
@fname varchar(40),
@lname varchar(40)
begin tran
select @ndentPrid = max(provider_id) from providerdnt
if @ndentPrid is null
set @ndentPrid = 1
else set @ndentPrid = @ndentPrid + 1

insert into dental..provider (provider_id, first_name, last_name, collections_go_to)
select @ndentPrid, first_name, last_name','YYYYYYYYYYYYYYYNNNNN' from inserted
commit tran

Will this do it or do I need to enforce some type of locking to handle the max value. There are no inserts into
table b directly only by the trigger insert on table a