It depends on whether you need to change the mapping for historical data or just for future data.
For future data (stored in new indices) it's sufficient just to put the new Index mapping in the cluster.
If you need a new mapping also for the historical data you will have to reindex the old data into new indices to get the new mapping. If you use Index Aliases, this is easy to do in production because users can then continue to query the old indices (through their aliases) until the new one is ready, then you just swap the alias and delete the old index. Just make sure to have enough disc space for the reindexing.