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Here are a few tips that may help decrease the query execution time for the array_agg function in Postgresql:

1. Use an index: Make sure that the columns you are aggregating are indexed properly to allow for quick retrieval.

2. Filter the data: Reduce the amount of data that needs to be aggregated by filtering out irrelevant or unnecessary rows. This will decrease the amount of work that the array_agg function needs to do.

3. Simplify the query: Check if there is a simpler or more efficient way to get the data you need. Sometimes a join or subquery may be faster than an array_agg function.

4. Increase resources: If the database is running on a machine with limited resources, consider increasing the CPU, RAM, or disk space to improve query performance.

5. Use a materialized view: If the array_agg function is used frequently on the same data set, consider creating a materialized view to pre-aggregate the data. This will reduce the amount of work the function needs to do at runtime.

6. Upgrade to the latest version: Postgresql releases updates regularly with performance improvements and bug fixes. Upgrading to the latest version may help improve the performance of your queries, including the array_agg function.