The following may help:

deaths
Source NZ Death Index
Surname KOST
Given Names Peter
Year of Death 1868
Record Number 409
Record Type Death registration
Age N/R
Location Hokitika

Source Karori Cemetery Office
Surname KOST
Given Names Annigje
Year of Death 1974
Record Type Crematorium
Age 74
Location Crematorium
------------------------------
marriages
Year 1956
Folio 02276
Surname KOST
Given Names Helma
Sex F
Spouse SOOLSMA, Joris Willem
----------------------------

Victoria (Aus) to NZ - Passengers 1852-1880

Name
KOST B.
Date of Arrival
1862
Number
18982
Age
36
Sex
M
Status
S
Occupation

Country

Accomodation
Fore
Ship
ALDINGA
Port of Departure
Melbourne
Date of Departure
22 Nov 1862
Port of Arrival
Port Chalmers
Source
PROV VPRS 948
LDS Film
0284491

Name
KOST C.
Date of Arrival
1867
Number
2965
Age
29
Sex
M
Status
S
Occupation
Miner
Country
SCT
Accomodation
Stg
Ship
RANGITOTO
Port of Departure
Melbourne
Date of Departure
16 May 1867
Port of Arrival
Picton
Source
PROV VPRS 948
LDS Film
0284499

Name
KOST Mrs
Date of Arrival
1867
Number
5155
Age
21
Sex
F
Status
M
Occupation

Country
ENG
Accomodation
Fore
Ship
EGMONT
Port of Departure
Melbourne
Date of Departure
24 Sep 1867
Port of Arrival
Nelson
Source
PROV VPRS 948
LDS Film
0284499
-------------------

NZ Probates

Name
KOST Charles
Place
Fitzroy, Victoria
Occupation
Bootmaker
Death Date
29 Mar 1902
Court
Wellington
Archives Reference
AAOM 6029 7983
Probate Number
7983
Filed Date
19 Sep 1902
Type
Intestate (Letters of Administration)
Comments

Further enquiries to
Archives NZ - Wellington
------------------------
[1881 NZ electoral roll, only one listing]
Electorate Picton
Number 474
Surname KOST
Given Names Charles
Nature Of Qualification Residential
Place Of Residence Picton
Occupation Shoemaker
---------------------------
[no Kost on the 1893 electoral roll]