If the limit is on the size of an array:
You will have to split the array into several job arrays. The --array parameter accepts values of the form <START>-<END> so you can submit four jobs:
sbatch --array=1-500 ...
sbatch --array=501-1000 ...
sbatch --array=1001-1500 ...
sbatch --array=1501-200 ...
This way you will bypass the 500-limit and still keep the SLURM_ARRAY_TASK_ID ranging from 1 to 2000.
To ease things a bit, you can write this all in one line like this:
paste -d- <(seq 1 500 2000) <(seq 500 500 2000) | xargs -I {} sbatch --array={} ...
If the limit is on the number of submitted jobs:
Then one option is to have the last job of the array submit the following chunk.
#!/bin/bash
#SBATCH ...
...
...
if [[ $((SLURM_ARRAY_TASK_ID % 500)) == 0 ]] ; then
sbatch --array=$((SLURM_ARRAY_TASK_ID+1))-$((SLURM_ARRAY_TASK_ID+500)) $0
fi
Note that ideally, the last running job of the array should submit the job, and it may or may not be the one with the highest TASK ID, but this has worked for all practical purposes in many situations.
Another options is to setup a cron job to monitor the queue and submit each chunk when possible, or to use a workflow manager that will that for you.