I just tested on ASA box the config you mentioned.
no context OLD-CONTEXT this will delete the context
context NEW-CONTEXT
allocate-interface GigabitEthernet0/0
allocate-interface GigabitEthernet0/1.1
config-url disk0:/OLD-CONTEXT.cfg give this command will reterive the config from the flash means what ever was in old context will use in new context.
==========================
prior to this i created the context name OLD-CONTEXT in ASA
!
context OLD-CONTEXT
allocate-interface eth1
allocate-interface eth0
CONfig-url disk0:OLD-CONTEXT.cfg
!
show context
Context Name Class Interfaces Mode URL
*admin default Routed disk0:/admin.cfg
OLD-CONTEXT default Ethernet0,Ethernet1 Routed disk0:/OLD-CONTEXT.cfg
!
creating the new context
!
no context OLD-CONTEXT
!
context NEW-CONTEXT
!
allocate-interface eth0
allocate-interface eth1
config-url disk0:/OLD-CONTEXT.cfg
!
changeto context NEW-CONTEXT
!
!
hostname OLD-CONTEXT (As the config are read from the flash they will show up as old hostname, you can change the old hostname to newhost name.)
!
interface Ethernet0
nameif outside
security-level 0
ip address 192.168.1.1 255.255.255.0
!
interface Ethernet1
nameif inside
security-level 100
ip address 172.16.1.1 255.255.255.0
please do not forget to rate.