The easiest solution is probably to add another container to your pod running socat or something similar and make it listen and connect to your local pod's IP (important: connect to the pod ip, not 127.0.0.1 if your database program is configured to only accept connections from the overlay network).
Then modify the service you have for these pods and add the extra port.
The example below assumes port 2000 is running your program and 2001 will be the port that is forwarded to 2000 inside the pod.
Example (the example is running netcat simulating your database program):
apiVersion: v1
kind: Pod
metadata:
name: database
labels:
app: database
spec:
containers:
- name: alpine
image: alpine
command: ["nc","-v","-n","-l","-p","2000"]
ports:
- containerPort: 2000
- name: socat
image: toughiq/socat
ports:
- containerPort: 2001
env:
- name: LISTEN_PROTO
value: "TCP4"
- name: LISTEN_PORT
value: "2001"
- name: TARGET_PROTO
value: "TCP4"
- name: TARGET_HOST
valueFrom:
fieldRef:
fieldPath: status.podIP
- name: TARGET_PORT
value: "2000"
---
apiVersion: v1
kind: Service
metadata:
name: database
spec:
selector:
app: database
ports:
- name: myport
port: 2000
targetPort: 2000
protocol: TCP
- name: socat
port: 2001
targetPort: 2001
protocol: TCP
externalIPs: [xxxxxx]