The prior answer does not actually answer the original stated question.
When Secondary NameNode performs checkpoint i.e. once it writes the updated fsimage to NameNode, does the old fsimage file gets deleted?
Yes, old fsimage files get deleted. However, a certain number of prior fsimage files will be retained. The exact number to retain is controlled by configuration property dfs.namenode.num.checkpoints.retained in hdfs-site.xml. If unspecified, then the default value is 2.
<property>
<name>dfs.namenode.num.checkpoints.retained</name>
<value>2</value>
<description>The number of image checkpoint files (fsimage_*) that will be retained by
the NameNode and Secondary NameNode in their storage directories. All edit
logs (stored on edits_* files) necessary to recover an up-to-date namespace from the oldest retained
checkpoint will also be retained.
</description>
</property>
The reason for retaining a few prior fsimage files is that it can be useful for post-mortem troubleshooting or in some disastrous cases as a way to restore a cluster to a prior state. (However, restoring an old fsimage will cause loss of all data that was saved after that checkpoint, so this is not standard operating procedure.)
