Where to install SSL Certificate for CURL request to external API

This is a bit of a strange situation, but I'm hoping someone here can provide some assistance. I have a legacy Java application that communicates with an external 3rd party API (UPS online tools). We recently received a notification that we need to update our server certificate by January 21 or our transactions will no longer work.

Our application is sending ssl requests to the external API via a curl request (it HAS to be curl due to the way this application is designed, it's a long story and not really relevant here). What I need to know is, where do I need to install the certificate? We have a front-end web server (Apache), a jboss backend, and an HAProxy service in between. The curl request is being made by the backend via a groovy class executing a curl command. Which of those is the external API looking for a certificate on when doing an ssl handshake?

In case it helps, here is what the groovy method looks like:

public String[] requestTracking(String url, String action, String trackingNumber, String access_license_number, String user_id, String password) {

        String request = """<?xml version="1.0"?>
            <AccessRequest xml:lang="en-US">
             <AccessLicenseNumber>${access_license_number}</AccessLicenseNumber>
            <UserId>${user_id}</UserId>
            <Password>${password}</Password>
            </AccessRequest>
            <?xml version="1.0"?>
            <TrackRequest xml:lang="en-US">
                <Request>
                <TransactionReference>
                    <CustomerContext>My Context</CustomerContext>
                    <XpciVersion>1.0001</XpciVersion>
                </TransactionReference>
                <RequestAction>Track</RequestAction>
                <RequestOption>${action}</RequestOption>
                </Request>
                <ShipmentIdentificationNumber>${trackingNumber}</ShipmentIdentificationNumber>
            </TrackRequest>
""";

        def command = [
            'sh',
            '-c',
            "curl -s -w '%{http_code}' '${url}' -X POST -d '" + request + "'"
        ];

        def proc = command.execute();
        def outputStream = new StringBuffer();
        def errorStream = new StringBuffer();
        proc.waitForProcessOutput(outputStream, errorStream);
        //      System.out.println("error: " + errorStream.toString());
        String result = outputStream.toString().trim();
        //split off the html status code
        String code = result.substring(result.length() -3);
        String body = result.substring(0,result.length() -3);

        String[] output = [code, body];
        return output;
    }